WASHINGTON — The Obama administration’s new plan to stimulate refinancings of FHA mortgages is likely to help large numbers of homeowners cut their monthly costs — even those who are deeply underwater. But it’s also likely to disappoint many borrowers who aren’t aware of the program’s fine print and end up missing an opportunity to switch into a loan with a rate below 4 percent.

To cut through the bureaucratic details, here’s a quick overview of the so-called “streamline refi” program and what it will take for you to qualify. First, the baseline criteria: Your current home loan must be FHA-insured and must have been put on the agency’s books no later than May 31, 2009. If you have a mortgage owned or backed by Fannie Mae, Freddie Mac, the Department of Veterans Affairs or private investors, you’re out.

The May 31, 2009, date is crucial. Your lender can tell you precisely when the FHA “endorsed” your loan for insurance. That is different from the dates you applied for your loan or closed on your house. If it turns out to be anytime later than May 31, 2009, you miss the cut.

You also need to have an unblemished record of on-time mortgage payments for the past 12 months. Maybe you were late occasionally a couple of years back. That’s OK. But the immediate past 12 months need to be pristine.

On top of that, if your refinancing does not provide you a net savings of at least 5 percent in your monthly principal, interest and mortgage-insurance payments, you won’t be eligible either. The program won’t take effect until June 11.

Those are the main hurdles. But they are substantial enough to exclude hundreds of thousands of current FHA borrowers who might otherwise like to refi. According to an FHA spokesman, Brian Sullivan, FHA has about 500,000 active loans in its portfolio that are eliminated from participation solely on the basis of the May 31, 2009, cutoff date.

Of those, an estimated 145,000 have mortgage interest rates higher than 5 percent — making them prime candidates for a refi if it weren’t for the cutoff date.

Now for the good stuff: Under the Obama plan, if you qualify on the criteria above, you get to breeze through the paperwork maze and underwriting hassles that come with any refinancing. The FHA streamline refi requires:

• No new verifications of your income or employment status. If you’ve been paying on time for a year, the presumption is that you’ve got the needed income.

• No new credit evaluation, credit reports or FICO scores.

• No new physical appraisal. The program generally accepts the appraised value of your home at the time you closed on your current FHA loan as good enough — even if you’re now in serious negative equity territory.

Along with the stripped-down underwriting, the new program also comes with valuable financial concessions. To sweeten the deal, the FHA has slashed its regular insurance-premium charges for qualified streamline applicants.

Take this hypothetical example provided by Paul Skeens, president of Colonial Mortgage in Waldorf, Md. Say you now have a $180,000 FHA loan at 5.25 percent that dates to March 2009. Your current monthly principal and interest payment is $993.93. With the addition of FHA’s mortgage-insurance premium costs of $82.50, your total monthly outlay is $1,076.43.

If you qualify for the new streamlined plan, you could lower your interest rate to 3.875 percent and your monthly principal, interest and mortgage insurance to $928.92 — an immediate savings of $147.51 per month or $1,770.12 a year. Over the next 60 months, you’ll save $8,850.06.

Not bad.

But why the May 31, 2009, cutoff? What about the thousands of responsible borrowers who happened to take out their FHA loans a little more recently, have paid on time and have rates higher than 5 percent? Why punish them?

Sullivan said it’s all about the traditional three-year “seasoning” period for mortgages during which the bulk of insurance claims — delinquencies and foreclosures — normally occur.

He denied industry rumors that the 2009 date had anything to do with the FHA’s policy of making partial refunds of upfront insurance premiums to borrowers who refinance during the first 36 months, which might cost the agency millions of dollars if more recent borrowers could qualify for the new program.

“How cynical,” he said in response to an email question on the refunds. “This is about easing the pressure on (borrowers) in a responsible way.” Saving money by cutting out more recent FHA borrowers “was never a consideration.”